We show that light spiraling like a tornado can be generated by superimposing abruptly auto-focusing ring-Airy beams that carry orbital angular momentum of opposite handedness. With different parabolic propagation trajectories, the superimposing ring-Airy beams are tailored to abruptly auto-focus at overlapping focal regions. This results in a complex wave with intense lobes that twist and shrink in an accelerating fashion along propagation. By achieving angular acceleration values that exceed 295     rad / mm 2 , these tornado waves can find numerous applications in laser trapping, direct laser writing, and high-harmonic generation.